The process of aligning images so that the corresponding features are related is called image registration. Image registration is one of the main problems in medical image analysis and it has received considerable attention for more than two decades. The numerous proposed image registration methods have not been shown to be optimal by any measure and they suffer from a common problem: ad-hoc assumptions. Furthermore, typically they rely on the optimization of an objective function, which inherently suffers from the problem of local minima and requires initialization. For these reasons the image registration methods proposed in the literature work only under special conditions and any deviation from these conditions causes the methods to fail. However, image registration is a mathematical problem that, if defined properly, can have an optimal solution. Mathematically guaranteed optimal image registration could have a considerable impact on medicine and almost any science and engineering field. The overall objective of this project is to obtain an explicit expression for the application-independent optimal image registration, which would avoid the problem of local minima and initialization. To achieve this objective the following specific aims are set. Aim 1: To identify the properties of image registration operators and define the optimal image registration operator. Aim 2: To determine the minimal achievable image registration error (the fundamental limit of image registration). Aim 3: To derive an explicit expression for the optimal image registration operator. Aim 4: To implement the optimal image registration method, apply it to a number of images of different modalities, and validate it using several studies. [unreadable] [unreadable] [unreadable]